Comparison of similar objects

We test the output of SINATRA with very similar objects. In this case, we generate a collection of spheres by perturbing their surfaces with independent normal noise. We then split the collection into two classes. There is no structural difference between any of these shapes, and hence we expect SINATRA to capture nothing.

Direction Parameters:

Simulation Parameters:

The reconstructed regions on a perturbed sphere are plotted below:

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The color scale is obtained as follows: we sort the features by RATE value, and go through them one by one, and reconstruct the subimage on the shape. The colors on the teeth describe when that vertex is born according to this procedure. For example, the 90 in the plot below indicates vertices that are born earlier. In particular, this vertex is first born when we reconstruct the subimage using the features with the top 10% of rate values. Conversely, the 10 in the color scale represents vertices that are born later, corresponding to vertices reconstructed after considering features with RATE value higher than the 90th percentile. [Apologies, I could not put this in the plot above].

We note that for the teeth, the colors on the scales were relative to birth time of the first reconstructed vertex on the tooth.

We see that the algorithm sets the birth time of the entire sphere quite late, which is some evidence for the null hypothesis that every feature is uninformative.

Comparing the scale to simulations

To gauge the results of the above reconstruction, we run the SINATRA procedure on spheres with cusps and compare the structure of the RATE values and reconstructed regions with those of the comparison of similar shapes above.

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The overlapped rate values are plotted below. The rate values for the simulated spheres with cusps are shown in black, while the rate values of the similar spheres are plotted in red

Comparison of less similar objects.

We also observe that SINATRA does not pick up any meaningful, distinguishing subimage.

## [1] "Running elliptical slice sampling..."

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## Warning in shade3d.mesh3d(x, ...): Default coloring for meshes changed in
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The color bar is unchanged from above.

Comparison of different objects

## Removed 19 duplicate 0 unreferenced vertices and 0 duplicate faces
## [1] "Running elliptical slice sampling..."

## Warning in shade3d.mesh3d(x, ...): Default coloring for meshes changed in
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## Warning in shade3d.mesh3d(x, ...): Default coloring for meshes changed in
## rgl 0.100.1